The mathemagician nodded knowingly and stroked his chin several times.
"You'll find," he remarked gently, "that the only thing you can do
easily is be wrong, and that's hardly worth the effort."

From The Phantom Tollbooth by Norton Juster

The Problem

The problem of interpreting voter intent when hand counting paper ballots
has led many people, over the past century, to press for the use of impartial
machinery in all ballot counting. The following quotations from the recount
battles following the controversial Florida presidential election in the
year 2000 expresses this in a very typical ways:

Voting machines are not Republican and
are not Democratic, and are not subject to
conscious or unconscious bias.

... I refer to this vote counting model as the "machine
model," because it counts as valid only those votes that the vote
tabulating machine can read and record. The machine model thus relies
on an objective tabulating machine that admits of no discretion to
count votes - if a vote is properly cast according to the instructions
given to the voter, the machine will count it.

Certainly voting machines are not subject to conscious bias because, simply
put, they are not conscious! Even the term unconscious bias does not apply
because we are reluctant to attribute unconscious behavior to things that
are incapable of conscious behavior. What I assert here is that the mechanical
vote tabulating systems in use today have variability in their vote counting
that is comparable to a degree of discretion and that, as a consequence,
the machine model is not an appropriate basis for answering the question
of what constitutes a valid vote on an optical mark-sense ballot.

The comparison of vote counting systems and gambling machines provides
some useful insight.
Gambling machines, even such trivial machines as dice, can certainly
be biased. Such biases can be accidental, the result of imperfect
construction, or, as in the case of loaded dice, they may be deliberate.
A voting machine may be biased in exactly the same ways!

In the remainder of this work, I will discuss the evolution of mark-sense
ballot scanning systems and the problems this technology poses, and then I
will compare some of the alternative legal models for regulating this
technology before proposing my own recommendations.
I want to emphasize that mark-sense ballot tabulation remains one of the
most reliable of voting technologies despite the technical and legal problems
that I will be emphasizing! The number of
votes brought into question by the problems pointed out here is likely to be
well below one percent of the vote in a properly administered election.

Some Definitions

Figure 1: An example Australian secret ballot.

Mark-sense ballots are a form of Australian secret ballot designed so that
the ballot may be machine counted. As such, they rest on the basic
Australian ballot, first used in 1858. Whether hand or machine
counting is used, voters using an Australian ballot are instructed to vote
using a prescribed mark written in the voting target.

voting target

The space on a ballot reserved for marks made by the voter in order to
indicate a particular preference with regard to an issue on the ballot.

prescribed mark

The form of mark a voter is instructed to make in the voting target
in order to cast a vote.

On the classic Australian ballot, the voting targets were either square
boxes or circles next to the name of each candidate, and the prescribed mark
was an X. When designed for use with optical mark-sense scanners, the
target is typically an oval or a broken arrow, and the prescribed mark is
either a blot filling the oval or a line connecting the two halves of the
broken arrow.
The following instructions for making a prescribed mark are typical of those
used for hand-counted Australian ballots:

168.576 Marking ballot ...

Sec. 576. (1) An elector, after having received a ballot or ballots, shall
enter a booth or voting compartment and, while there concealed from view,
shall vote the ballot or ballots by making a cross or a check mark in the
square at the left of the names of those candidates for whom the elector
desires to vote ...

When counting ballots, we do not limit our count to ballots containing
prescribed marks; instead, we count those containing acceptable marks.

acceptable mark

Any mark on a ballot that meets the legal requirements to be counted as
a vote.

Obviously, under any reasonable code of law, voters who follows the
instructions for making a prescribed mark should automatically produce
acceptable marks, but the prescription does not usually delimit all of
the forms of marking that are and are not acceptable. The Michigan code
cited above illustrates this; while voters can easily follow these
instructions, when it comes time to count the votes, the vote counters
must have answers to these questions:

What is a cross?

What is a check mark?

What does it mean for this mark to be in the square?

Michigan law answers these questions as follows for hand-counted paper ballots:

168.803 Counting and recounting of votes ...

Sec. 803. (1) Except as otherwise provided in this act, the following rules
shall govern the counting and recounting of votes: ...

(b) A cross, the intersection of which is within or on the line of the
proper circle or square, or a check mark, the angle of which is within
a circle or square, is valid. Crosses or check marks otherwise located
on the ballot are void.

(c) Marks other than crosses or check marks used to designate the intention
of the voter shall not be counted.

(d) A cross is valid even though 1 or both lines of the cross are duplicated,
if the lines intersect within or on the line of the square or circle.

(e) Two lines meeting within or on the line of the square or circle, although
not crossing each other, are valid if it is apparent that the voter intended
to make a cross. ...

If the instructions for making the ballot are typical of those for optical
mark-sense ballots, to fill in the oval next to the candidate's name using
black ink or pencil, we must answer a different set of questions. For example,
we might be tempted to ask:

How much of the oval must be filled for it to be counted as a vote?

What colors or shades of grey are considered to be black?

As with the acceptable mark rules for hand-counted Australian ballots,
the above questions are legal questions, in the sense that their answers
are typically set by statute or administrative rules, and they can be
answered without regard to any particular tabulating machine! On the other
hand, if the law says one thing and the machine judges marks differently,
the machine may not be appropriate for use in this jurisdiction.

Figure 2: Venn diagram of the universe of all ballot markings.

Our use of tabulating machines requires more terminology!
Tabulating machinery counts only those marks actually detected; these
are among the detectable marks on the ballot.
Some marks will be reliably detectable, while others will be
marginal.

detectable mark

A mark on a ballot that can be detected as a vote by a vote
tabulating machine.

reliably detectable mark

The form of mark on a ballot that will be detected and counted each
and every time the ballot is run through a tabulating machine, irrespective
of which voting target is being marked, and irrespective of the particular
machine being used.

reliably ignored mark

The form of mark on a ballot that will never be detected or counted no
matter when the ballot is run through a tabulating machine, irrespective
of which voting target is being marked, and irrespective of the particular
machine being used.

marginal mark

A mark on a ballot that may or may not be counted, depending on which
voting target is marked, depending on what vote tabulating machine is used,
and depending on when the count is made.

Well formulated voting laws governing the use of machine-counted ballots
ensure that the prescribed mark will be reliably detected, and they ensure
that, in practice, the vast majority of acceptable marks are reliably
detectable and that the vast majority of reliably detectable marks are
acceptable.

The machine model, as defined in
Touchston and Shepperd vs. McDermott identifies acceptable marks with
detectable marks, and it assumes that there will be no marginal marks.
Equivalently, it assumes that all detectable marks are reliably detectable.
Furthermore, this model is only just if the voter can easily determine,
by eye, whether his or her mark is detectable. As we will see, all of these
assumptions are false!

No technology based on machine-counted Australian
secret ballots can eliminate all marginal marks, and with many voting
systems, visual inspection by the person making the mark is not sufficient
to determine if the mark will or will not be detectable! We must, therefore,
allow for the possibility of marks that are false positives and
false negatives. These are standard statistical terms, but in the
context of vote counting, we may define these terms for
misinterpreted marks as follows:

false positive mark

A mark on a ballot that does not meet the legal definition of an
acceptable mark but that is, on some occasion, detected by a vote tabulating
machine as a vote. False positive marks may be marginal marks or reliably
detectable marks.

false negative mark

A mark on a ballot that meets the legal definition of an
acceptable mark but that is, on some occasion, not detected by a vote
tabulating machine. False negative marks may be marginal marks or they
may be reliably ignored.

misinterpreted mark

A mark on a ballot that is misinterpreted by a vote tabulating machine;
this term includes both false positive and false negative marks.

Ideally, we would hope for vote tabulating machines that guaranteed that
there would be no marginal marks, no false positive marks and no false
negative marks. Unfortunately, there is no technology for machine tabulation
of Australian secret ballots that can accomplish this, for two different
reasons! First, no technology can eliminate the possibility of a marginal
mark, and second, mark-sensing machinery cannot generally duplicate the
judgement of a human examining the ballot. To understand these two
limitations, we need to understand something about mark sensing technology.

Mark Sensing Technologies

The original mark-sensing technology dates back to the 19th century, when
it was developed for use with the very earliest of facsimilie machines;
these relied on the ability of the fax scanner to detect the electrical
conductivity of marks on the surface. First, this was done with insulating ink
on conductive stationary -- they actually used tinfoil stationary in some
early systems.
In 1937, IBM introduced the Type 805 Test Scoring Machine for processing
standardized educational tests, and shortly after this, they began to offer
mark-sense options on punched-card forms used in business applications.
These systems used the slight electrical conductivity of pencil
marks on paper to detect marks. The very first mark-sense ballots, tried
in Kern City, California, in 1962, may have used electrical mark-sensing,
but I have been unable to find details about these early trials.

Optical mark-sensing also dates back to the facsimilie machine, and by
the 1920's, it had been developed to the point that grey-scale photographs
could be reliably transmitted by telephone and radio. In the 1950's, a
group working under Professor E. F. Lindquist at the
University of Iowa developed an optical mark-sense scanning system to
score the ACT college entrance examination, and this scanner is the
ancestor of the experimental mark-sense scanners used for vote counting by
Westinghouse Learning Corporation in the 1970's. American Information Systems,
an ancestor of Election Systems and Software, licenced this technology from
Westinghouse when the former abandoned this venture.

Discrete-sensor Infrared Mark Sensing

The first generation of mark-sense scanners used for vote counting use
infrared light. Such a scanner has an array of sensors, typically packed
on 1/4 inch or 1/2 inch centers, but sometimes fewer. Each sensor consists
of an infra-red light-emitting diode and phototransistor, matched to each
other so that the peak sensitivity of the phototransistor is close to the
wavelength emitted by the diode.
Typically, the light-emitting diode and phototransistor
are mounted side-by-side with a barrier between them so that the only
light reaching the photosensor will be that reflected from the ballot.
The ballot feed mechanism inside the ballot scanner
feeds the ballot past the sensor array in such a way that some sensor in
the array scans down each column of voting targets on the ballot.
The
Election Systems and Software
Models 550 and 650 optical mark-sense
ballot tabulating machines are typical of this class of scanners, although
unlike the illustration in Figure 3, they use fiber optics between the
light-emitting diodes, the photosensors and the ballot.
Chatsworth Data Corporation
also makes scanners that are similar the illustration in Figure 3.

Figure 3: The mechanism of an optical mark sense scanner
using a single discrete photosensor for each column of marking positions.

Figure 4: A W600 sensor assembly.
Device gift of John V. McMillin

Where graphite pencil marks are scanned, it is important to note that such
a mark can be burnished to a high sheen. As a result, when the viewing angle
and illumination angle are similarly oblique, a pencil mark can be more
reflective than unmarked paper. Some scanners have illumination and sensing
angles carefully adjusted to avoid being mislead by this. The Westinghouse
model 600 scanning head illustrates this. This was developed by John V.
McMillin for test scanning, and then (in the late 1970s) used in the W600B
ballot scanner.
Here, the LEDs illuminating the page are at roughly 45 degrees to the paper,
while the photodiode is mounted perpendicular to the illuminated spot.

Note that the voting targets on infrared optical-scan ballots are typically
printed in a carefully selected ink that is invisible to the sensors; in
visible light, this ink frequently appears red, as shown in Figure 3.
Typical scanners have sensors over many different columns of potential
voting targets, both because of the evolution of such scanners from test
grading machines, and because the extra sensors allow more flexible ballot
layouts, for example, allowing the voting targets to be to the left or
right of the candidate names and allowing the ballot to be arranged in
two or three columns.

In addition to the sensors over the columns of voting targets on the ballot,
the machine typically has one or two sensors that detect index marks on
one or both edges of the ballot; these are needed because the machine cannot
see the voting target itself, so it uses the index marks on the edge to tell
it when it is looking at a row of potential voting targets. Additional index
marks on the top and bottom are used to detect misaligned ballots; only if all
of these marks are seen does the scanner consider the ballot to be correctly
aligned.

The area of the ballot seen by each sensor is a narrow stripe running along
the direction of ballot motion through the scanner. Although these areas are
shown with sharp borders in Figure 3, the areas seen by
real sensors usually have diffuse borders. As a result, each sensor
is usually most sensitive to marks that include the center of the stripe it
sees, and less sensitive to marks falling to the sides. In
formal mathematical terms, the sensing profile is typically described by
something close to a Gaussian function.

The Effect of Sensor Geometry

Figure 5: The actual voting targets on the example ballot.

The index marks along the vertical edges of the ballot and positions of the
sensors along the sensor bar define the potential voting targets on
the ballot. In the example shown in Figure 5, there are 48 potential
voting targets arranged in 6 columns, corresponding to the 6 sensors
that are available to scan columns of targets, and arranged in 8 rows because
there are 8 index marks down the edge of the ballot. The intersection of
each row, as defined by index marks on the ballot edge, with each column, as
defined by the position of a sensor, defines a potential voting target.

The most common form of voting target printed on the ballot is an oval,
but the actual area that the scanner sees on any particular scan of the
ballot is the rectangular intersection of the area scanned by one sensor
and the row defined by the index marks! Perfect mechanical alignment is
impossible, so from one scan of the ballot to the next, the sensor may
follow a slightly different path across the ballot. All of the possible
paths of the sensors
across the ballot typically required to be within the area defined by the
index marks at the top and bottom of each column, so the effective voting
targets are the rectangular areas at the intersection of the rows and
columns defined by the index marks. These are shaded in Figure 5.

Typically, we number the potential voting targets by counting down the columns,
leftmost column first, as shown in Figure 5. The scanner hardware actually
detects any mark in any voting target, and it is up to the vote tabulating
software to ignore
marks in the targets that are not part of this election. In the example
shown in the figure, only positions 5 through 7 and 28 through 31 are
relevant. It is very likely that a scan of the example ballot will detect
marks in positions 13 and 21, because the name "Washington" passes through
these, but the software should ignore this!

It is worth noting that paper ballots change size slightly with changes in
humidity! Commercial printers use the rule of thumb that a 10% increase
in relative humidity causes paper to expand by about by one part in 1000;
as a result, the size of a piece of bone-dry paper could expand by as much
as 1% as it picks up moisture in an extremely humid environment. This
comes to 1/10 inch in 10 inches, while many mark-sense voting targets are
about 1/8 inch in their short dimension!

The early mark-sense scanners used for scoring tests solved the problems
caused by humidity changes by storing all test papers in a controlled
atmosphere for some time prior to tabulation, but on modern mark-sense vote
tabulators, the design accommodates humidity changes by spacing the
sensors to the midrange of variation in paper size and using voting targets
that are wider than the sensors.

Figure 6: The effect of changing humidity, somewhat
exaggerated, on the alignment of photosensors with voting targets
and index marks.

If one or more of the top or bottom index marks are not seen on a pass
through the scanner, the scanner typically stops with an error message
indicating a misfeed. This could be due to an extreme dimensional change
in a ballot, for example, because the humidity is too high for reliable
scanning or because the paper has been crumpled and then flattened, or it
could be because the paper passed through the scanner
on a diagonal.

The fact that sensing tracks are narrower than the voting target means that
a mark may be seen on one pass through the scanner and not on a later pass,
perhaps because of a humidity change from one pass to the next. The fact
that a ballot may be on a slight diagonal as it is scanned introduces the
possibility that identical marks in two different places on the ballot might
be counted differently, even when they are seen by the exact same photosensor.

Figure 7: The areas seen by photosensors 2 and 5
on a ballot that was fed through the machine on a slight diagonal.

Several marks have been made on the ballot shown in Figure 7 to illustrate
some of the marginal marks that are possible because of the geometry of the
ballots and photosensors:

A reliably detectable mark for G. Washington was made by
carefully following the instructions for the prescribed mark.

A mark for A. Lincoln. With most optical mark-sense vote tabulators,
this mark will be reliably detectable because it is dark and spans all possible
tracks of the detector over the ballot.

A marginal mark by the write-in blank for President. Although this oval
mark is entirely outside of the voting target printed on the ballot, parts of
the oval are within the rectangular area that is actually scanned. Had the
sensor passed over the center of the target on this pass, the parts of this
mark it sees would all be outside the actual target area. The farther off
center the scan is, the more likely this mark is to be seen!

A marginal for N. Longworth. Although this
vertical mark covers a larger percentage of the voting target than the
horizontal mark for Lincoln, it will only be seen if the sensors happen to
pass over the left side of the target. On the pass through the scanner
illustrated in Figure 7, this mark will not be detected.

A marginal mark for S. Rayburn. This small dot will not be seen on
the pass through the scanner illustrated here.

A marginal mark by the write-in blank for Congress. This small dot
is identical to that by S. Rayburn, but on this pass, it will be detected.
In fact, this mark will be seen by the sensor as a larger mark than the one
for A. Lincoln!

Conclusion:
The fraction of the target area filled in by the voter does not
necessarily
determine which marks will be counted on a particular mark-sense
ballot tabulating machine; in fact,
many machines will detect and count some marks that are entirely outside
of the target printed on the ballot.

Conclusion:
It is quite possible for a ballot to be counted in two different
ways on two successive passes through the same voting machine.

The fact that such scanners can reliably detect horizontal lines in the
voting target but cannot reliably detect vertical lines in the target
has led to the development of an alternative style of voting target with
an alternative statement of the prescribed mark: The voting target is
a broken arrow and the prescribed mark is a line connecting the two halves
of the arrow. This is common with the Optech line of
precinct-count ballot tabulators originally made by
Business Records Corporation and now available from
Sequoia Voting Systems
and from
Election Systems and Software.

The example ballot shown in Figure 8 is entirely interchangeable with
the example used in the previous figures in the sense that it could be
scanned on the same ballot scanners with no change to the ballot
tabulating software. The only differences between these styles of
voting target lie in the area of human factors. While the oval target is
familiar from other domains such as educational testing, the broken arrow
was found by some early users to invite fewer marginal marks from voters.
Whether this remains true today and whether it is relevant with more
modern scanning mechanisms is not clear.

The Effect of Sensor Threshold

Each particular sensor in a mark sensing scanner will have a threshold.
Marks that are below this threshold will not be sensed by this sensor,
while marks above this threshold will be sensed. It is also theoretically
possible that there will be marks that are just at this threshold, but this
possibility does not produce a significant number of marginal marks.

The two primary problems leading to marginal marks that can be traced to
sensor thresholds are as follows:

In general, no two sensors will have identical thresholds! This follows
from the simple fact that sensors are physical devices and the fact that, in
general, no two physical objects are identical in any attribute. We can work
to make our sensors as nearly similar as possible, but the greater the
similarity we demand, the higher the price.

In general, no sensors will have a constant threshold! This follows
from the simple fact that sensors are physical devices and the fact that,
in general, all physical objects change with time. Dirt and scratches slowly
accumulate on the photosensors, and temperature variations change the behavior
of the electronics. We can try to build devices that are stable over time,
but the greater the stability we demand, the higher the price.

Figure 9: Marginal marks that result from different sensor
thresholds.

With the first generation of discrete sensor optical mark-sense ballot
scanners, it was common to have a small trimmer control for each sensor
on the scanner. Prior to each election, a technician must run a special
form through the scanner printed with a special test pattern while monitoring
the output of the sensor electronics. This allows the technician to adjust
the trimmer controls in order to set the thresholds of all of the sensors
to acceptable values. It is not difficult to use this technique
to set all of the sensors within a few percent of each other.

More recently, discrete sensor systems have been designed that are self
calibrating. These typically compare the darkness of black index marks
with the brightness of the adjacent paper as they scan each ballot, and then
set the threshold to an appropriate intermediate point between these.
The newest central count mark-sense scanners from
Election Systems and Software
use this approach.
An even better approach would be to print, on each ballot, calibration marks
that are just above and just below the threshold. With widely available
electronics, this approach can be used to calibrate things to within
about 1 part in 250, and with modestly more expensive electronics, it
can be used to calibrate the sensors to within about 1 part in 4000.

Figure 10: Marginal marks that result from different line
width thresholds.

It should be noted that each sensor in a discrete sensor optical mark-sense
scanner has two different thresholds, one for the darkness of the mark and
one for the width of the mark. Both dark narrow marks and broader light
marks may be acceptable. The relation between these two is usually not
simple; rather, the darkness required is usually set at such a level that
a broad smudge resulting from a poor erasure will not be seen as a mark,
while the scanner will usually detect and count a single dark pencil
stroke across the marking area.

Note that all of the marks shown in Figure 10 are of identical darkness, and
are as dark as the darkest marks in Figure 9. Had these marks been of marginal
darkness, only the widest would be likely to be sensed at all.

Conclusion:
Neither the darkness of the mark nor the width of the mark, taken alone,
determine which marks will be counted on a particular mark-sense vote
tabulating machine.

Discrete-sensor Visible Mark Sensing

The fundamental problem with infra-red mark sense scanners is that they
sense marks using a wavelength of light that the human eye cannot see!
As a result, some marks that are clearly evident to the human eye will be
invisible to the photosensors in the scanner, while other marks may well
be visible to the photosensors but invisible to the human eye!

Figure 11: Color sensitivity of different photosensors.

The classic instructions for mark-sense forms say "use number two soft lead
pencil". This instruction is safe because pencil graphite is equally dark
in the visible and infrared wavelengths. The same is true of india ink, but
this cannot be said of inks based on organic dies. A black ink made
from a mixture of red, blue and green organic inks may look identical to black
india ink, but it may be invisible to an infra-red sensor.

If voters always voted using the marking device provided at the polling place,
this would not lead to problems, but absentee voters frequently reach for any
available pen or pencil, and if the point breaks off of the pencil provided
in the voting booth, voters will frequently use their own pens or pencils,
particularly when lines are long and the polling place officials are harried.

The solution is obvious! We can replace the infra-red light-emitting diodes
and phototransistors in the mark sensor with light-emitting diodes and
photosensors that work with visible light. Reliable red light-emitting diodes
and phototransistors sensitive to red light were available within a few
years of the original generation of infrared sensors, and like infra-red
sensors, these are generally insensitive to light red ink, allowing the
scanner to easily ignore the printed red voting targets while reliably
sensing marks made by the voter.

The documentation for the
mark-sense readers from
Chatsworth
is quite open about the impact of the shift from infra-red to visible
illumination; the data-sheets for all of their standard readers end with a
footnote saying:
"The I.R. option limits the marking instruments but allows for greater
selection of background colors for printing. The Visible Red option
allows for a greater range of marking instruments but limits the background
printing to a 'Warm Red' color." Few vendors of voting systems have
traditionally given this much detail.

Curiously, the very first generation of optical mark-sense scanners used
for scoring the ACT exam in the 1950's used white light from conventional
incandescent lamps. The
problem with incandescent lamps is that they burn out too frequently,
and as a result, only when white LEDs came on the market did some
optical mark-sense scanners return to the use of white light.

Conclusion:
The apparent darkness of a mark, as seen by the human eye, does not
necessarily determine whether that mark will be counted on a particular
mark-sense vote tabulating machine.

Fax-bar Mark Sensing

The advent of inexpensive facsimilie machines in the 1980's opened a new
path to mark-sense tabulation.
from Alexander Bain's first fax machine in 1843 to the present, all fax
machines have incorporated page scanning mechanisms of some sort. In the new
generation of inexpensive fax machines introduced in the late 20th century,
the scanning mechanism is packaged as a fax bar, or more formally
as a contact image sensor. The fax bar consists
of a linear array of integrated circuit photosensors plus a source of
illumination for
the copy being scanned. The fax bars used in facsimilie
machines typically have close to 200 photosensors per inch; similar sensor
arrays made specifically for scanning mark-sense documents are available with
resolutions closer to 16 per inch.

Typical modern fax bars include either a cold cathode fluorescent lamp or
an array of light emitting diodes for illumination. When light emitting
diodes are used, they are usually green because green is a rare ink
color; black, blue and red are far more common.
The cold-cathode lamps used in fax bars are very
small, 1/8 inch diameter is typical, and they produce the same quality of
white light associated with common household fluorescent lamps. As a result,
fax bars are typically able to sense those marks that most people
would judge to be intentional.

Figure 13: Partial pixelized image of a scanned ballot.

When a ballot is scanned using a fax bar or similar scanner, each sensor is
checked repeatedly as the ballot is moved past the sensors, and the result is
processed by the computer attached to the scanner as a pixelized image.
Figure 13 shows the result of pixelizing a small
part of the ballot image for the scanner and ballot shown in Figure 12.

At a low level, the sensors used in fax bars report the brightness of each
pixel in the document, but because today's facsimilie machines do
not transmit the brightness of each pixel, this information is frequently
simplified to a simple indication of black and white before the pixel data
is given to the computer. For each column of pixels, we can therefore find
the brightness threshold above which the sensor will report no mark, and
below which it will report that there is a mark.

Because we are using visible light sensors, most fax bars on today's market are
able to see voting targets printed in colors such as red, although some cannot
sense a light shade of pink or green (depending on the color of LED used in
the fax bar). In the example in Figure 13, we have assumed that
the sensors are sensitive to the shade of ink used in the voting target, and
as a result, blank voting targets are seen by the scanner as having around 14
dark pixels. In contrast, the marked target shown in the figure has 27 dark
pixels.

The number of pixels reported as being dark when
scanning any particular mark on the ballot may vary from one scan to the next
depending on how the grid of pixels happens to align with the mark. Shifting
the mark half a pixel left, right, up or down may add or subtract a few pixels
from the total. As a result, some scans of an unmarked voting target might
show as few as 12 pixels, while others might show as many as 16 pixels.

Given that our example marked target has 27 dark pixels and our example
unmarked target has only 14 dark pixels, an obvious strategy to use in with
this scanning system is to declare a voting target to be voted if more than,
say, 18 pixels in the vicinity of the target are found to be dark. Such a
threshold strategy requires no attempt at complex image analysis! All
that is needed is software in the voting system that finds the
index marks, and then using that information, finds the locations on the ballot
where voting targets are expected.

Conclusion:
The use of advanced technologies such as visible light sensing and
fax bars cannot eliminate the class of marginal marks; at best,
such technologies can reduce the number of marks that might be marginal.

The threshold method outlined here is probably typical of today's ballot
scanners, but it is important to emphasize that voting system manufacturers
generally do not reveal anything about how their scanners identify marks!
Frequently, the publically available documentation on the scanners does not
even reveal whether they use discrete sensors or fax bars.

The
Election Systems and Software
PBC 100 precinct-count optical mark-sense ballot tabulating machine is an
exception. This machine is advertised as using an intelligent mark
recognition algorithm based on image processing. For classical elliptical
voting targets, this algorithm uses exactly the kind of pixel-counting
threshold method documented here; for Optech-style broken arrow voting
targets, it takes advantage of the boldly printed half-arrows by using them
as index marks to locate the precise top and bottom bounds of each voting
target.

These relatively crude schemes for identifying
marks on the ballot using a fax bar scanner are generally significantly
better at reading the ballot than a discrete sensor scanner. They can easily
distinguish between small dots in the voting area and a line crossing the
target in any direction, and they are generally insensitive to the direction
of the line. Because the designers of fax bars are very sensitive to the
requirements of fax machines, these sensors are generally good at reading
any reasonable weight of pencil stroke or any common shade of ink, and they
are generally good at ignoring all but the worst erasures.

In theory, it would be possible to use advanced computer-based image processing
methods to do even better. Imagine software that located the voting target
and all marks near it on the ballot using image processing techniques and then
classified the marks as spots, pen or pencil strokes, or other marks. Having
located the apparent pen and pencil strokes, the software would then classify
them as dashes, checks, Xs, etc before applying a standard derived from the
applicable law in order to determine which are votes.

One problem with the use of such advanced image processing algorithms is
that most voting system manufacturers do not have the necessary expertise
to oversee development of such software. Furthermore, the inclusion of
such complex software in a voting system significantly increases the
difficulty of certifying the software for the voting application.

The different sensors in a fax bar or similar scanning system generally
have different thresholds! This is an unavoidable consequence of the
integrated circuit manufacturing process used to make the sensors,
and unlike scanners that use discrete sensors, we can
do little to calibrate the sensors in the fax bar. Instead, we rely on the
fact that each voting target is seen by a large number of sensors; for example,
the low resolution scanner in Figure 12 sees each target with 6 or 7 sensors,
depending on how the ballot is aligned. So long as the variations in sensor
threshold are random, the more sensors that see each voting target, the more
likely it is that each voting target will be seen with a similar range of
sensor thresholds.

Figure 14: Fiducial marks for use with a pixel scanner.

It is perfectly feasible to use a fax bar or a more advanced image sensing
scanner with a ballot that uses index marks such as those commonly used with
discrete-sensor scanning systems, but when new ballot formats are developed
for use with these modern scanning technologies, it is common to use a
different approach to locating the voting targets on the ballot.

Figure 14 illustrates a ballot design appropriate for such an environment.
Here, instead of marking each row and column with index marks, the ballot
contains only four special marks, in the extreme corners of the ballot. Such
marks are called fiducial marks. The software used to interpret the pixelized
image of the ballot first locates these fiducial marks and then measures from
these in order to locate the voting targets. This approach can easily correct
for ballots that are fed into the scanner on a diagonal and it can correct
for uniform changes in ballot dimensions caused by humidity.

Another common feature found on ballots designed to be read on fax bar
scanners or other scanners that pixelize the image prior to processing is
a bar code to identify, for example, the precinct or ballot style. Simple
codes for identifying this information have been used with older generations
of ballot scanning systems, for example, by using wide and narrow index marks
along the top or bottom rows of the ballot, or by reserving a column of the
ballot for a code track, as is usually done on the
Election Systems and Software
Models 550 and 650 optical mark-sense ballot tabulating systems.

It is important to note that the developers of ballot tabulators that use
fax bars or other image sensing technologies generally work to maintain
compatibility with earlier discrete scan mark sensors. While it would be
possible, in theory, to build an image sensing mark-sense tabulators that
requires a very accurate reproduction of the prescribed mark, in general,
this is not done. If it were done, the new tabulating system would reject
votes that were accepted by the earlier tabulating system, and this would
be unacceptable to most jurisdictions.

Image Scanners for Mark Sensing

Today, fax bars are in competition with an even higher performance class
of scanning mechanisms, those designed for image scanning. Todays image
scanning mechanisms have resolutions of 300 pixels per inch or more, and
with complete scanners available at costs of under $100, it is not surprising
to find these being incorporated into new ballot tabulators.

Aside from a higher resolution, the most important feature of image scanning
mechanisms is that they deliver either an overall brightness report for each
pixel, in the case of black and white scanners, or separate red, green and
blue brightness reports for each pixel in the case of color scanners. Given
brightness reports for each pixel, the software can easily compare the paper
background to the index marks in order to calibrate the sensors for the
extremes of black and white found on the ballot. The ballot shown in
Figure 14 has no index marks, but the heavy horizontal line that separates
the ballot heading from the body of the ballot can serve exactly the same
purpose.

With color scanners, it is possible, in theory, to distinguish between special
inks and the colors of pen or pencil that are required, but I have seen no
evidence that the voting systems on the market today are doing this.
As with fax bar scanners, however, the vendors do not generally disclose to
the states the actual method they use to distinguish between marked and
unmarked voting targets.

Conclusion:
The exact same ballot format may be used with a variety of different
mark-sense ballot tabulating machines, where the different tabulating
machines count marks in distinctly different ways, applying different
criteria to determining which marks are and are not counted as votes.

Other Sources of False Positives

There are several sources of false positives that plague all optical mark-sense
scanners. The most important of these are the result of ballot defects.
The following types of ballot defects are relatively rare, but all of them occur
occasionally.

Printing errors

All printing processes produce occasional smudges and ink splatters.
Small defects the size of a pencil mark can easily escape the kind of quality
control methods traditional in the printing industry, yet if these accidentally
fall in a voting target, they can be read as a vote by the scanner.

Defects in the paper

Ballots are usually printed on relatively high quality paper or lightweight
cardstock, but this does not guarantee that the paper will be free of defects.
The most common defects found in such paper are flecks of foreign
material, usually a light brown color. If such a fleck occurs in a voting
target, it can be read as a vote by the scanner.

If we demanded that all ballots be scanned prior to issue to the voter and
we reject any that contain votes on this preliminary scan, we would eliminate
the few ballots that are accidentally pre-marked in the manufacturing process,
but there are other sources of marks that make such a precaution largely
irrelevant.

Accidents

Whenever people handle pieces of paper, there is the possibility that
they will leave marks. Generally, ballots are handled by at least two
people at the polling place, the voter and the worker who hands the ballot
to the voter. In central count systems and absentee voting, even more hands
typically touch each ballot. While we can ask everyone involved to work
with clean hands, there is still the possibility that, for example, a pencil
point will break somewhere nearby and that a ballot or stack of ballots will
be set down on the broken pencil point, leaving a mark.

Hesitation marks

One particular class of accidental mark is of special importance.
Many people, when holding a pencil while reading a text, use the pencil point
as a pointer, resting it on the paper beside each line while reading that
line. Unfortunately, wherever the voter rests the pencil point, it
will generally make a faint mark, and the obvious place to rest the pencil
point beside a line on the ballot is in the voting target for that line.

Most accidental marks are small spots, and most mark-sense ballot tabulating
systems have thresholds set so that they ignore typical hesitation marks, but
some voters make darker hesitation marks than others. Voters with mild
vision problems frequently find it helpful to use a pointer when reading,
and the same mild vision problem that leads a voter to use the pencil as
a pointer may make that voter unable to see the marks it leaves.

Erasures

While the instructions frequently prohibit erasures, most mark-sense
vote tabulating machines are fairly good at disregarding cleanly erased
marks. Some erasures, however, are dark enough that they will be read as
a mark.

The instructions forbidding erasure are frequently quite blunt, sometimes
to the extent that some voters may believe that erasures actually
invalidate their ballots.

Do not erase or cross out. Obtain a new ballot if you make an error.

Official Ballot, General Election, Nov 7, 2000, Walton County, Florida.

Unfortunately, while it is easy to state a prohibition against erasure or
correction, it is extremely difficult to enforce it. At a polling place where
the lines are long and the polling place officials are harried, voters may
hesitate to ask for replacement ballots and instead opt to erase, and it may
be completely impossible for an absentee voter to obtain a replacement ballot.

Conclusion:
If erasures are forbidden by law, we must face the fact that most
of the available mark-sense vote tabulating systems will disregard
most competently made erasures. If, on the other hand, we allow
erasure, we must face the fact that some erasures will be so darkly
smudged that most mark-sense scanners will detect them as marks.

If a voter casts a vote in some race and the scanner encounters a false
positive in some other voting position in the same race, it will generally
convert the voter's intended mark into an overvote. Ballot scanners that
can reject overvoted ballots and return them to the voter for correction can
protect voters against such problems, but this is only helpful for
precinct-count voting systems and offers no protection for absentee voters
or those voting in jurisdictions that use central-count systems.

Even when precinct-count vote tabulating machines are used, some voters will
leave the polling place without properly feeding their ballots into the
machine or without noticing that the machine has not accepted their ballot.
As a result, polling place workers need to have procedures to deal
with ballots that have been abandoned by the voters.

When absentee ballots are sent through the postal system, there has always
been the possibility that they will be damaged in transit. Because such damage
is not the fault of the voter, most states have instituted carefully
thought-out procedures for reconstructing the voter's intended ballot when
a damaged absentee ballot is received.

Conclusion:
If we apply the procedures for correcting damaged absentee ballots
to all of those ballots where a vote tabulating machine detects
overvotes and the voter is unavailable to make corrections, we can
interpret apparent overvotes due to false-positives caused by
accidents, defects or erasures,
thus offering these voters at least part of
the protection available to voters who use precinct-count ballot
tabulating systems.

Legal Considerations

There is a strong tradition in American case law that argues in favor of
a very forgiving model of what marks on a ballot are to be accepted as votes.

Ballots will not be treated as void merely because of technical
or minor errors or because of irregular or unauthorized markings
which appear to have been innocently made as the result of
accident, awkwardness, nervousness, inattention, mistake,
ignorance, or physical infirmity, if the lawful intent of the
voter can be ascertained ...

Corpus Juris Secundum Volume 29, Elections, Page 494.

If the voter's intention can be
ascertained with reasonable certainty, ordinarily the ballot
should be given effect and counted in accordance with that
intention, provided the voter has substantially complied with
statutory requirements and no essential mandate of the law is
thereby violated.

Corpus Juris Secundum Volume 29, Elections, Page 496.

Because the right to vote is so highly prized, these statutes must be
construed liberally in favor of giving effect to the voter's choice,
and every vote enjoys a presumption of validity.

Devine vs. Wonderlich 268 NW2d 620, 623 (Iowa Supreme Court, 1978)

The Michigan law cited previously is quite narrow in its definition of
an acceptable mark, but it includes one clause that is very permissive:

168.803 Counting and recounting of votes ...

Sec. 803. (1) Except as otherwise provided in this act, the following rules
shall govern the counting and recounting of votes:

(a) If it is clearly evident from an examination of any ballot that
the ballot has been mutilated for the purpose of distinguishing it
or that there has been placed on the ballot some mark, printing,
or writing for the purpose of distinguishing it, then that ballot is
void and shall not be counted. ...

(g) Erasures and corrections on a ballot made by the elector in a
manner frequently used for this purpose shall not be considered
distinguishing marks or mutilations.

Clause g gives the voter the right to correct a mismarking in
any manner that is "frequently used for this purpose." Frequently
used correction methods include erasure, crossing out, scribbling
over and a variety of other markings that have obvious meaning to a
human reader but may be very difficult for a machine to evaluate.

Manufacturers of optical mark-sense ballot tabulating systems have consistently
responded to this tradition of lenience by designing successive generations of
mark-sense scanners that accept wider and wider varieties of non-prescribed
markings while still successfully ignoring hesitation marks, erasures and
small defects in the ballot itself. Thus, while early discrete scan ballot
tabulators counted some circled voting targets by accident, more recent
pixel-based tabulating systems intentionally scan an even larger area
around the voting target in order to deliberately detect and count such
nonstandard marks.

Despite these efforts, today's mark sense vote tabulating systems do not
and cannot be expected to count some of the apparently bizarre marks seen
on real ballots and widely reported during the contested 2000 presidential
election in Florida. When poorly designed ballots or poorly written
instructions lead voters to misinterpret the prescribed mark in wild ways,
for example, connecting the point of the arrow to the candidates name instead
of connecting the two halves of the arrow, or coloring in the space between
two index marks, the machine cannot be expected to fully automate the lenient
vote counting rules that judicial precedents demand.

The battle over the contested presidential election in Florida has added
a significant new dimension to the question of what ballot markings should
be accepted as votes:

Florida's basic command for the count of legally cast votes
is to consider the "intent of the voter." ... This is unobjectionable as
an abstract proposition and a starting principle. The problem inheres
in the absence of specific standards to ensure its equal application. The
formulation of uniform rules to determine intent based on these recurring
circumstances is practicable and, we conclude, necessary.

Prior law had effectively demanded a lenient and therefore potentially
subjective interpretation of markings on ballots in those cases where
automatic machinery was unable to interpret the vote or where
the count made by such machinery was being challenged. It was quite evident
in the Florida recounts of 2000 that this standard allowed considerable
latitude, so markings accepted as votes by one recount board were being
rejected by another recount board. The supreme court found this lack of
uniformity to be an unconstitutional violation of the equal protection
clause of the constitution.

Conclusion:
If it is unconstitutional for one human recount board to count
as a valid vote a mark that would not be accepted by another
recount board, the very same
considerations bring the machine model into question because
of the possibility of marginal marks being interpreted differently
by different machines or even by the same machine on a different
trial.

The Florida legislature responded to Bush vs. Gore and more generally to
the controversy surrounding the contested general election of 2000 by
enacting sweeping changes to their election law, including a provision
calling for a mandatory manual recount of close elections:

102.166 Manual recounts.--

(1) If the second set of unofficial returns ...
indicates that a candidate for any office was defeated or eliminated by
one-quarter of a percent or less of the votes cast for such office ...
the board responsible for certifying the results of the vote on such race
or measure shall order a manual recount of the overvotes and undervotes
cast in the entire geographic jurisdiction of such office or ballot measure.

(2)(a) If the second set of unofficial returns ...
indicates that a candidate for any office was defeated
or eliminated by between one-quarter and one-half of a percent of the
votes cast for such office ...
[the] candidate, [or] the political party of such candidate ... is
entitled to a manual recount of the overvotes and undervotes cast in
the entire geographic jurisdiction of such office or ballot measure, ...

(3)(a) Any hardware or software used to identify and sort overvotes and
undervotes for a given race or ballot measure must be certified by the
Department of State as part of the voting system ...

That the total number misinterpreted marks
should normally be under one-quarter of one percent of the total number
of votes cast for an office.

That the total number misinterpreted marks will never exceed
one-half of one percent of the total.

That the only ballots requiring manual recounting in order to resolve
misinterpreted marks will be those containing either overvotes or undervotes.

It is curious that the number of overvotes and undervotes itself does not
trigger a manual recount! For example, if the working hypothesis is that
misinterpreted marks will generally be detected as overvotes or undervotes,
then why not have a mandatory recount when the sum of overvotes plus undervotes
in an election exceeds the margin of victory for the apparent winner in the
election?

Is it sensible to assume that misinterpreted marks will show up as overvotes
or undervotes? We can identify the following mutually
exclusive possibilities for false positives and false negatives in a normal
vote-for-one election:

A false positive occurs in a race where the voter intended to abstain.
This converts the voter's vote from an undervote in that race to a vote for
some candidate, and this ballot will not be hand examined under Florida's
recount statute.

A false positive occurs in a race where the voter cast a vote for some
other candidate. This converts the vote to an overvote,
and it will be resolved by hand examination under Florida's rules.

A false negative occurs in a race where the voter intended to cast a single
vote. In this case, the outcome will be an undervote,
and it will be resolved by hand examination under Florida's rules.

A false negative occurs in a race where the voter intended
an overvote. This error will lead to one of the voter's votes being
counted.

If we assume that very few voters intentionally abstain, and that few
voters intend to cast overvotes, then the Florida rules will result in
human inspection of the vast majority of misinterpreted marks. These
assumptions generally hold for top-of-the-ticket races for offices such
as the presidency or the governorship.

The problem with Florida's law arises in bottom-of-the-ticket races for
minor local offices. It is common for the majority of the voters to abstain
from such races, and when this occurs, the majority of the false positives
will be counted as legitimate votes and will never be inspected in a hand
recount.

Conclusion:
If hand examination of ballots is limited to those ballots that are
classified as overvotes and undervotes, the recount will correct
the vast majority of misinterpreted marks in top-of-the-ticket
vote-for-one races.

Conclusion:
If hand examination of ballots is limited to those ballots that are
classified as overvotes and undervotes, the recount will not properly
account for false positives in bottom-of-the-ticket races.

The fact that the majority of voters commonly cast undervotes
in bottom-of-the-ticket elections provides the answer to the question
posed above about having an automatic recount when the sum of overvotes
plus undervotes exceeds the margin of victory. Such a standard would be
very expensive because it would force recounts in almost all minor races.
We can, however, demand an automatic hand recount if the number of overvotes
taken alone exceeds the victory margin of the apparent winner. Given that
modern precinct-count voting systems can automatically return overvoted
votes to the voter, we can do even better!

Conclusion:
We can reasonably ask that all ballots on which the vote tabulating
machinery detects an overvote be subject to human inspection. Ideally,
the voter should do this, taking advantage of precinct-count election
systems, but if this is not possible, for example, with absentee
ballots or with central-count systems, we can require hand interpretation
of such ballots.

Florida's revised election law lays down the following framework
for establishing
state administrative rules to define what is and is not an acceptable marking
on the ballot:

102.166 Manual recounts.--

(5)(a) A vote for a candidate or ballot measure shall be counted
if there is a clear indication on the ballot that the voter has made
a definite choice.

(b) The Department of State shall adopt specific rules for each
certified voting system prescribing what constitutes a
"clear indication on the ballot that the voter has made a definite
choice." The rules may not:

1. Exclusively provide that the voter must properly mark or
designate his or her choice on the ballot; or

2. Contain a catch-all provision that fails to identify specific
standards, such as "any other mark or indication clearly indicating
that the voter has made a definite choice."

In effect, these rules require the production of a catalog of acceptable
ballot markings as part of the administrative rules for each
approved voting systems. This approach to meeting the mandate of the
Supreme Court has merit, but in light of the conclusions we have already
drawn, it raises some thorny issues:

How do we anticipate the likely non-prescribed markings?

How do we deal justly with a non-prescribed markings that was not
anticipated by the administrative rules and yet has an obvious meaning?

How do we ensure that the rules for one approved voting system are
comparable to those for another approved voting system?

The newspaper sponsored examinations of Florida's ballots after the
disputed 2000 general election revealed several consistent patterns of
mismarkings that were immediately proposed for incorporation into
Florida's administrative rules; the result of this approach is a set of
rules that deals effectively with the errors voters have made in the
past. Unfortunately, some of these errors were the result of specific
misinterpretations of voting instructions that were invited by poor ballot
design or badly worded instructions, for example:

1S-2.027 Clear Indication of Voter's Choice on a Ballot

(2) The following are guidelines for determining on
an optical scan voting system whether or not there is a
clear indication on the ballot that the voter has made a
definite choice: ...

(e) If a voter circles or underlines the name of a
party next to a candidate's name, the vote shall count
for that candidate.

This rule covers a specific response by voters to the fact that, in many
Florida counties, three letter party abbreviations were placed in a column
to the right of the candidate names, while voting targets were placed in a
column to the left, with the size and shape of the three letter abbreviation
very similar to that of the voting target. Furthermore, the instructions
on the ballot included only a filled target, not an empty one, and the
example filled target was to the right of the text explaining it.

Figure 15: A badly designed ballot inviting a specific error.

This design flaw was present only in the ballots used by some of the
counties that used the
Accu-Vote
line of precinct-count optical mark-sense ballot tabulators made by
Global Election Systems,
among them the ballots used in Citrus (.03%),
Leon (.01%) and St. Lucie (.3%) counties. Not all Global
customers made this mistake! Others used various strategies
to discourage this voter error, including Calhoun (0%), Hernando (.009%),
Monroe (0%), Polk (.002%) and Walton (.01%) counties.
The percentages listed after the county names give the fraction of voters
who made this mistake, computed from the
Miami Herald, Knight Ridder, USA Today
data on voter errors;
I have not seen sample ballots for the other Florida counties using the
Accuvote system.

There is no way to anticipate, in advance, all non-prescribed markings that
voters will make on ballots, and if some of these markings are specific
responses to flaws in the ballot design or instructions, we cannot anticipate
the markings without also anticipating the mistakes we will make in ballot
design. Florida's revised election law, by prohibiting a catch-all provision,
makes it very difficult to deal justly with such problems!

Michigan election law suggests an excellent solution to the problem of
avoiding the catch-all provision that Florida Law and the Supreme Court
decision have forbidden while not requiring anticipating every voter error.
At the end of a section that otherwise leans toward a rather strict
version of the machine model, we find this:

168.803 Counting and recounting of votes; rules; intent of voter.

(2) If an electronic voting system requires that the elector place a
mark in a predefined area on the ballot in order to cast a vote, the
vote shall not be considered valid unless there is a mark within
the predefined area and it is clearly evident that the intent of the
voter was to cast a vote. In determining intent of the voter, the
board of canvassers or election official shall compare the mark
with other marks appearing on the ballot.

In contrasting this with Florida's law, we see that Michigan does not provide
for nonstandard markings outside the voting target, while Florida does.
On the other hand, so long as the mark is within the voting target, Michigan
avoids an enumeration of marks and instead takes advantage of an important
feature of a general election ballot -- the fact that the ballot generally
contains multiple races, and therefore, that it will generally contain several
attempts by the voter to cast votes.

Conclusion:
We can distinguish between a deliberate but nonstandard mark and
an accident by looking at how the voter marked other voting targets
on the same ballot. If a similar mismarking is repeated in other
races in a manner otherwise consistent with the requirement for voting,
whether or not the mark is in the voting target, it is extremely
likely that the mark is an expression of voter intent.

Florida's law calls for "specific rules for each certified voting system,"
raising the question of how we ensure that the specific rules for one voting
system are comparable to the rules for another.
The proposed administrative rules that respond to this clause address all
optical mark-sense voting systems as if they were the same. This is
probably the correct response to a flawed law, despite the fact that
different voting systems may have distinctly different responses to identical
markings within similar voting targets on similarly constructed ballots.

Conclusion:
Voters do not respond to technical details of how mark-sense scanners
operate, they only respond to the instructions they are given and to
the layout of the ballot. Therefore, the rules governing the
interpretation of voter markings should depend only on these factors
and not on the details of the scanning mechanism.

A far greater problem with uniformity arises in the area of ballot layout
and voter instructions. Florida's election law requires the following:

101.151 Specifications for ballots.--

(8)(a) The Department of State shall adopt rules prescribing a uniform
primary and general election ballot for each certified voting system.
The rules shall incorporate the requirements set forth in this section
and shall prescribe additional matters and forms that include, without
limitation:

1. Clear and unambiguous ballot instructions and directions;

2. Individual race layout; and

3. Overall ballot layout.

(b) The department rules shall graphically depict a sample uniform
primary and general election ballot form for each certified voting system.

As we have seen, there was a specific design flaw in the 2000 general election
ballots in several counties using the Accu-Vote line of tabulating systems.
This flaw clearly traces to a "sample ... general election ballot form" that
was distributed to the counties that use the Global Accu-Vote scanners.
Some counties followed this sample form without modification,
while others made one or another change to this form in order to reduce the
likelihood of error. This ballot design error was not apparent on the two
other optical mark-sense tabulating systems used in the state, and therefore,
the class of voter error this design error elicited was not a problem in
counties using the other systems. Sadly, in many cases, those counties
made other errors.

Conclusion:
If it is unconstitutional for one ballot marking to be counted
differently in two different jurisdictions, we must also ask if
it is constitutional to use substantially different ballots and
substantially different voting instructions in different jurisdictions,
particularly when the differences are entirely avoidable and not
necessary consequences of different voting systems.

Human Factors

Knowing that all systems for scanning physical ballots are able to
misinterpret the voter's intent, we design ballots and voting instructions
that reduce the likelihood that voters will make reliably detectable marks
for those candidates they wish to vote for and will assure that all other
marks on their ballot are reliably ignored. One of the central problems we
face today is that we have no institutions in place for determining how well
we are succeeding at this!

We need to know what fraction of the voters have difficulty following the
voting instructions, and how they misinterpret the instructions. We need to
know the frequency of false positive and false negative marks on ballots
cast by real voters, and we need to classify these marks by their causes.
Aside from false positives caused by ballot defects, all of these are human
factors issues! That is, they turn not on the details of the technology, but
on how people react to the technology.

Recounts provide us with some help here, and the data from the 2000 general
election in Florida is exceptionally useful in this regard, but that is just
one sample point.

Conclusion:
We need to routinely monitor the performance of our election
systems, gathering statistics from every election in every county
on the number of over and undervotes so that we can constantly monitor
the quality of our ballot designs and voting instructions. At the very
least, these numbers should be brought forward in the official canvass
of every election.

Conclusion:
We need to routinely conduct hand recounts of some small but significant
number of ballots in order to monitor the extent to which our ballot
tabulating machines are successfully counting the marks voters
are actually making on the ballots. An appropriate approach might be
to require a hand count of all votes in one randomly selected race
in one randomly selected precinct after every election.

Ideally, the over and undervote numbers, along with any discrepancies found
in these manual recounts, should be brought forward to a state or national
agency that searches for correlations between the voting system used and the
problem rate observed. The results of these studies would be of incomparable
value to all of those who administer voting systems.

Recommendation

It is important to remember that optical-scan mark-sense ballot tabulating
systems remain one of the best approaches to vote counting that we have.
Unlike direct-recording electronic voting systems, scanners rely on the
original paper records of voter intent as recorded by the voters themselves,
and as a result, a purely software based attack on the integrity of the
voting system is impossible. The voter's intent is recorded in a form that
most people are comfortable interpreting, with no recourse to obscure
technologies that involve chad or even more obscure technologies.

Therefore, we must find ways to improve the conduct of elections
that use mark-sense tabulating systems. The improvements we need fall into
two distinct categories. First, we need to improve our control over the
voting systems themselves, and second, we need to improve the laws governing
the use of those systems.

Voting Machine Standards

As has been mentioned, the current generation of mark-sense voting systems
are being sold to states, counties and municipalities with no documentation
of the standards the machine uses to determine what is a mark. We must
require full disclosure of the following:

Figure 16: Appropriate documentation of the spectral response
of a mark-sense scanner.

What kind of light is the system using for mark sensing? Ideally,
the vendors should be required to state far more than the wavelength of peak
sensitivity or worse yet, a simple statement that the system uses some
unspecified visible or infrared light. I would prefer it if the vendors
gave the spectral response of the system as a graph that was clearly labeled
with the visible color spectrum for comparison purposes, as illustrated in
Figure 16. The spectrum in the figure is typical of the spectra expected from
scanners that use fluorescent light sources. Note that this is not simply
a graph of the output spectrum of the light source in the scanner, nor is it
simply a graph of the spectral sensitivity of the photosensors, but rather,
it is a graph of the product of these two!

What criteria does the ballot tabulator use to distinguish between
acceptable marks and unacceptable marks? This involves answers to a number
of subsidiary questions such as: Is the entire voting target inspected on
each scan, or just a portion, as in a typical scanner based on discrete
sensors? Is the area scanned larger than the target printed on the ballot?
Is the mark recognition system more sensitive to marks in one region of
the voting target or in one orientation than in another region or orientation?

What kinds of marks are reliably detectable by this ballot tabulator,
what kinds of marks are reliably ignored, and what kinds of marks are marginal.
Ideally, the documentation for the scanner should include samples of each
class of mark. These serve to illustrate, by example, the criteria the
system uses, and they also serve to illustrate how close to marginal the
prescribed mark is and how reliably the system is in ignoring marks such as
erasures and hesitation marks.

Conduct of Elections

The fact that mark-sense ballot tabulating equipment occasionally miscounts
votes can be dealt with in several ways. In Florida, for example, when there
is a recount, all overvoted and undervoted ballots are subject to hand
examination. Michigan's law is closer to the machine model, but it too
allows a hand recount and it too allows the examiners during a recount to
interpret as votes at least some marks that the machine may have ignored.

In order to ensure an accurate count, we need to regularly audit our voting
systems, we need to ensure that marginal marks are judged by humans. In order
to accomplish these goals, we must require the following:

Whenever practical, we must return overvoted and blank ballots to
the voter for correction. This will allow the voter to correct overvotes,
both those that were caused by false positives and those resulting from
ineffective attempts to correct errors. This is easily done with
precinct-count voting systems, but it is not possible with mail-in absentee
ballots.

When it is impractical to return an overvoted or blank ballot to the voter
for correction, or when a voter refuses the opportunity to change a ballot
that was returned by a precinct count scanner, this ballot should be subject
to hand examination. This requires that central-count equipment sort out all
overvoted and blank ballots, and this requires that such ballots found at
polling places be set aside for inspection. The methods of ballot enhancement
or duplication used for absentee ballots that have been damaged in the mail
should apply to all such ballots.

Assuming that we have appropriately uniform rules for hand-interpretation of
marks on ballots, and that these rules give the voter broad latitude for
expressing his or her choice on the ballot, the above rules give central-count
voters almost as much protection as they give voters who use precinct-count
systems.

To ensure that there are always a number of election workers who have
had experience hand counting ballots, and to ensure that the counts reported
by our ballot tabulating equipment are accurate reflections of the legal
standards for what constitutes a vote, we should require routine hand counting
of a small fraction of the ballots in every election. For example, we could
require a hand recount of one randomly selected race in one randomly selected
precinct after every election, with all discrepancies reported to the state.
If the state finds that some voting system has a uniformly higher discrepancy
rate than others, it should trigger reexamination and possible discontinuation
of the use of that system!

To ensure that all ballots are accounted for, and in order to monitor
the frequency of voter difficulty, we should require that the number of spoiled
ballots be carried forward through the canvassing process in every election.
Ideally, the total number of votes for each candidate in a race, plus the
number of overvotes and undervotes in that race, plus the number of spoiled
ballots, plus the number of challenged ballots, plus the number of unreturned
absentee ballots ought to equal the number of ballots given to voters. This
is a strong protection against many forms of election fraud. In addition, the
number of spoiled ballots is a measure of the frequency with which voters
had difficulty and therefore a measure of the likelihood that other voters
may have had problems that went undetected.

When to Recount

Recounts are expensive, and therefore, no election administrator wants to
encourage them. In order to reduce the frequency of recounts, some states
require those requesting a recount to post bond, and many states forbid a
recount unless the election is sufficiently close. The problem is, we must
permit and in fact encourage recounts if it is even remotely possible that
the miscounted votes in a race could change the outcome.

It is appropriate to allow recount requests when the election is
close, for example, if the margin of victory of the apparent winner is
smaller than some set percentage. Given that it is common for recounts
to come within 1 vote in 5000 of the first count in the absence of any
accounting or procedural errors, allowing recounts when there is a margin
of under 1 percent seems generous.

There are some benefits that go to participants in an election even
if they lose. For example, if a party gains 5 percent of the vote for any
statewide office, some states grant that party special status -- automatic
placement on the ballot in the next election, for example. Therefore, we
need to allow recounts if a candidate comes within range of such a threshold.
For example, we could allow a recount if a candidate comes within 1 percent
of the number of votes required to achieve any statutory benefit from
the election.

We need some way to allow recounts if there is evidence that there
were problems with the election! As many as 10% of the voters in some
Florida counties made errors on their ballots in the 2000 general election.
The count of spoiled ballots plus ballots that required enhancement or
duplication provides a measure of the frequency with which voters had
difficulty. If this number is high, there is a high likelihood that other
voter difficulties went undetected. Therefore, if this number exceeds some
threshold, no matter how close the election was, we should allow a recount.
For example, we may allow a recount when the number of spoiled ballots
plus ballots that required enhancement or duplication exceeds 1% of the total.

How to Recount

One purpose of a recount is to assure that an eccentric count of marginal
votes is not a significant component of the outcome of the election. To
ensure this, we must demand the following:

The vote tabulating machines used in a recount should be tested and
recalibrated prior to the recount in order to ensure that their sensing
thresholds are correct. In addition, if possible, the tabulating machines
used for the recount should not be the same machines used in the original
count; this ensures that the ballots will be seen by different scanners and
it maximizes the likelihood that marginal marks will be interpreted
differently on the recount.

Given that overvotes have been dealt with prior to the first count,
therefore correcting most false positives,
it is appropriate to hand inspect all ballots that show an undervote in the
race being recounted in order to catch and correct most false negatives.

If the number of spoiled ballots plus the number of ballots requiring
enhancement or duplication exceeds the margin of victory of the apparent
winner, it is highly likely that other ballots contain errors that did not
lead to over or undervotes; in this case, it seems appropriate and perhaps
necessary to allow a hand recount of all ballots cast in the race.

Hand Counting Rules

Whenever a ballot is examined by hand, whether to deal with a blank or
overvoted ballot that the voter has not corrected during the first count,
during a routine hand recount conducted for auditing purposes, or during a
recount conducted at the request of a party to the election, the same
criteria should apply to interpreting voter marks.

The class of acceptable marks must include all reliably acceptable
marks that are not the result of errors in ballot printing, erasures or
other obvious corrections, or stray marks.

The class of acceptable marks must include those marginal and
reliably ignored marks that appear to be deliberately made as indications
of voter intent. A mark should be accepted as an indication of voter
intent when similar marks have been used in multiple contests on the
ballot and where most such marks conform to the other rules of the election,
for example, voting for no more than one in most vote-for-one races.

Attempts at erasures, striking out an otherwise acceptable mark, and
written notations indicating errors should be accepted at face value,
despite rules forbidding erasure or correction.

Defects in the ballot and stray marks that do not meet the criteria for
acceptable marks should be ignored.

First posted on the web, February 2002; this document was originally
prepared in conjunction with the author's work on the 2001 Iowa Ad Hoc
Election Reform Task Force, convened by Iowa Secretary of State Chet Culver
to examine the need for Iowa to respond to the problems exposed by
the general election of 2000.